What is the solution for x(dy)/(dx)+y=4x+1,y(1)=8 ?

The solution for x(dy)/(dx)+y=4x+1,y(1)=8 is y=2x+1+5/x

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x(dy)/(dx)+y=4x+1,y(1)=8

x \frac{d y}{d x} + y = 4 x + 1, y (1) = 8

y = 2 x + 1 + \frac{5}{x}

Solution steps

x \frac{d y}{d x} + y = 4 x + 1

Solve linear ODE:

y = 2 x + 1 + \frac{5}{x}

y = 2 x + 1 + \frac{5}{x}

x \to 6 lim (x - 5)

\int (x + 1) d x

x \to - 2 lim (\frac{x + 1}{x ^{3} + 8})

\frac{d}{d x} ((- 2 cos (2 x) - sin (3 x))^{2})

x \to 4 lim (\frac{2 x ^{3} - 128}{x - 2})

What is the solution for x(dy)/(dx)+y=4x+1,y(1)=8 ?
The solution for x(dy)/(dx)+y=4x+1,y(1)=8 is y=2x+1+5/x